Thank you for the responses and I will definitely do a bit of tinkering with the order in which I will see the national park! Would you suggest more in the region of a week spent in Yellowstone?
As for the rental prices; I knew about the fees and they may just be something we have to deal with unless I do all the driving as there are situations with our postgraduate study that will have to be sorted out! The US citizen would have a car, however, we wouldn't feel confident in its abilities to last driving in the desert (especially in 3-4 years time!).
In terms of the 90 days I was just worried that if we planned a whole country trip then we would spend a lot of time on the road. As much as we don't mind the driving and will actually enjoy it, we were wanting to have relaxing stops for multiple days at a time.
Colin